Problem: Simplify the following expression: $\dfrac{70r}{14r^2}$ You can assume $r \neq 0$.
$ \dfrac{70r}{14r^2} = \dfrac{70}{14} \cdot \dfrac{r}{r^2} $ To simplify $\frac{70}{14}$ , find the greatest common factor (GCD) of $70$ and $14$ $70 = 2 \cdot 5 \cdot 7$ $14 = 2 \cdot 7$ $ \mbox{GCD}(70, 14) = 2 \cdot 7 = 14 $ $ \dfrac{70}{14} \cdot \dfrac{r}{r^2} = \dfrac{14 \cdot 5}{14 \cdot 1} \cdot \dfrac{r}{r^2} $ $\phantom{ \dfrac{70}{14} \cdot \dfrac{1}{2}} = 5 \cdot \dfrac{r}{r^2} $ $ \dfrac{r}{r^2} = \dfrac{r}{r \cdot r} = \dfrac{1}{r} $ $ 5 \cdot \dfrac{1}{r} = \dfrac{5}{r} $